Uncertainty and Inference

To build up empirical intuition about data, comparisons, and the mechanics of regression modelling, in previous workshops we have focused on understanding the calculation and interpretation of regression coefficients. These ‘point estimates’ may appear as reliable and certain answers to concrete research (sub)questions, but in fact they are a well-intended guess mired in uncertainty. Can they really tell us something reliable about the phenomenon under study in our population of interest, beyond the sample of data that we used to calculate them? Here’s where it becomes essential to develop our understanding of statistical theory that we have so far avoided. Thinking carefully about probability, uncertainty and the challenges of drawing inferences beyond one’s available data will help better understand our – and other researchers’ – results and the claims that can be made on their back.

Essential readings

(Access links through Canvas - Newcastle University login required)

Spiegelhalter (2020) The Art of Statistics: Learning from Data:

• CHAPTER 3 | Why Are We Looking at Data Anyway? Populations and Measurement
• CHAPTER 7 | How Sure Can We Be About What Is Going On? Estimates and Intervals
• CHAPTER 9 | Putting Probability and Statistics Together
• CHAPTER 10 | Answering Questions and Claiming Discoveries

Further readings

Spiegelhalter (2020) The Art of Statistics: Learning from Data: (Access through Canvas - Newcastle University login required)

• CHAPTER 11 | Learning from Experience the Bayesian Way

• CHAPTER 12 | How Things Go Wrong

• CHAPTER 13 | How We Can Do Statistics Better

Çetinkaya-Rundel & Hardin (2024) Introduction to Modern Statistics:

• Chapter 12 (“Confidence intervals with bootstrapping”)
• Chapter 13 (“Inference with mathematical models”)
• Chapter 24 (“Inference for linear regression with a single predictor”)
• Chapter 25 (“Inference for linear regression with multiple predictors”)
• Chapter 26 (“Inference for logistic regression”)
• Chapters 16 – 22 (“Statistical Inference” section)